Exam 16: Superposition and Standing Waves

Two sound waves, one wave is given by y₁ = p_o sin (kx - $\omega$ t) and the other by y₂ = p_o sin (kx - $\omega$ t + $\pi$ /4). The phase constant resulting from the interference of the two waves is

Two trumpet players are both playing a pitch with a frequency of 440 Hz, corresponding to the musical pitch A above middle C. However, one of the trumpet players is marching away from you so that you hear a beat frequency of 4 Hz from the two trumpets. With what speed is the departing trumpet player moving away from you? (The speed of sound in air is 340 m/s)

A clarinet, which is essentially a tube that is open at one end, is properly tuned to concert A (440 Hz) indoors, where the temperature is 20ºC and the speed of sound is 340 m/s. The musician then takes the instrument to play an outdoor concert, where the temperature is 0ºC and the speed of sound is 331 m/s. What is the frequency of the A played on the cold clarinet? (Ignore any thermal changes in the body of the clarinet itself.)

What is the phase difference at any given instant between two points on a wave which are 1.52 m apart if the wavelength of the wave is 2.13 m?

Use the figure to the right to answer the next problems. The graph shows three harmonics. -If f_o is the fundamental frequency, the three harmonics and their relative intensities can best be written as